Ellebigemia
contestada

1) Is it possible to have a function f defined on [ 2 , 4 ] and meets the given conditions?
f is continuous on [ 2 , 4 ), minimum value f(4)=2, and no maximum value.

2) Is it possible to have a function f defined on [ 4 , 5 ] and meets the given conditions?
f is continuous on [ 4 , 5 ], takes on no rational values.

3) Is it possible to have a function f defined on [ 2 , 5 ] and meets the given conditions?
f is continuous on [ 2 ,5 ] and the range of f is an unbounded interval.

Respuesta :

Nirina7
the answer

1 and 2 are possibles, but 3 is not.
MrRoyal

The possibility statements are:

  1. Possible
  2. Possible
  3. Not possible

Statement 1

The function is defined on [2.4]

The above means that, the minimum is 2, and the maximum is 4

However, since the function is continuous at [2,4), the close bracket ")" means that the function extends indefinitely i.e. no maximum.

Hence, this statement is possible

Statement 2

The function is defined on [4.5]

The above means that, the minimum is 4, and the maximum is 5

However, since the function is continuous at [4,5], the close brackets "[" and "]" mean that the function have finite values

Hence, this statement is possible

Statement 3

The function is defined on [2,5]

The above means that, the minimum is 2, and the maximum is 5

However, since the function is continuous at [2,5], the close brackets "[" and "]" mean that the function have finite values and it has bounded intervals

Hence, this statement is not possible

Read more about continuous functions at:

https://brainly.com/question/20089539